Hadassah bowls a strike on $60 \%$ of the frames she bowls. Let $F$ be the number of frames Hadassah bowls until she bowls a strike. Assume the results of each frame are independent.

Find the probability that it takes Hadassah less than 3 frames to bowl her first strike.
You may round your answer to the nearest hundredth.
$$
P(F

Q: Hadassah bowls a strike on $60 \%$ of the frames she bowls. Let $F$ be the number of frames Hadassah bowls until she bowls a strike. Assume the results of each frame are independent. Find the probability that it takes Hadassah less than 3 frames to bowl her first strike. You may round your answer to the nearest hundredth. \[ P(F<3)= \]

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the probability of Hadassah bowling a strike in one frame, which is given as $60\%$ or $0.6$. ‖ ‖ step 2 ⋮ Calculate the probability of Hadassah not bowling a strike in one frame, which is $1 - 0.6 = 0.4$. ‖ ‖ step 3 ⋮ Calculate the probability of Hadassah bowling her first strike in the first frame, which is the same as the probability of a strike in one frame, $P(F=1) = 0.6$. ‖ ‖ step 4 ⋮ Calculate the probability of Hadassah bowling her first strike in the second frame. This is the probability of not bowling a strike in the first frame and then bowling a strike in the second frame, $P(F=2) = 0.4 \times 0.6$. ‖ ‖ step 5 ⋮ Add the probabilities of bowling a strike in the first frame and in the second frame to find the total probability of bowling a strike in less than 3 frames, $P(F<3) = P(F=1) + P(F=2)$. ‖ ‖ step 6 ⋮ Calculate $P(F<3) = 0.6 + (0.4 \times 0.6)$. ‖ ‖ step 7 ⋮ Simplify the expression to find $P(F<3) = 0.6 + 0.24 = 0.84$. ‖ ‖ step 8 ⋮ Round the answer to the nearest hundredth, which gives $P(F<3) = 0.84$. ‖ ∻[1] Answer∻ ⚹ $P(F<3) = 0.84$ ⚹ ∻Key Concept∻ ⚹Calculating cumulative probability of independent events⚹ ∻Explanation∻ ⚹The probability of Hadassah bowling a strike in less than 3 frames is found by adding the probabilities of independent events: bowling a strike in the first frame or not bowling a strike in the first frame but bowling a strike in the second frame.⚹◊What is the formula to calculate the probability that it takes Hadassah less than 3 frames to bowl⍭ Generate me a similar question◊

Question

Hadassah bowls a strike on $60 \%$ of the frames she bowls. Let $F$ be the number of frames Hadassah bowls until she bowls a strike. Assume the results of each frame are independent.

Find the probability that it takes Hadassah less than 3 frames to bowl her first strike.
You may round your answer to the nearest hundredth.
$$
P(F<3)=
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Calculate the probability of Hadassah bowling a strike in one frame, which is given as $60\%$ or $0.6$. ‖ ‖ step 2 ⋮ Calculate the probability of Hadassah not bowling a strike in one frame, which is $1 - 0.6 = 0.4$. ‖ ‖ step 3 ⋮ Calculate the probability of Hadassah bowling her first strike in the first frame, which is the same as the probability of a strike in one frame, $P(F=1) = 0.6$. ‖ ‖ step 4 ⋮ Calculate the probability of Hadassah bowling her first strike in the second frame. This is the probability of not bowling a strike in the first frame and then bowling a strike in the second frame, $P(F=2) = 0.4 imes 0.6$. ‖ ‖ step 5 ⋮ Add the probabilities of bowling a strike in the first frame and in the second frame to find the total probability of bowling a strike in less than 3 frames, $P(F<3) = P(F=1) + P(F=2)$. ‖ ‖ step 6 ⋮ Calculate $P(F<3) = 0.6 + (0.4 imes 0.6)$. ‖ ‖ step 7 ⋮ Simplify the expression to find $P(F<3) = 0.6 + 0.24 = 0.84$. ‖ ‖ step 8 ⋮ Round the answer to the nearest hundredth, which gives $P(F<3) = 0.84$. ‖ ∻[1] Answer∻ ⚹ $P(F<3) = 0.84$ ⚹ ∻Key Concept∻ ⚹Calculating cumulative probability of independent events⚹ ∻Explanation∻ ⚹The probability of Hadassah bowling a strike in less than 3 frames is found by adding the probabilities of independent events: bowling a strike in the first frame or not bowling a strike in the first frame but bowling a strike in the second frame.⚹◊What is the formula to calculate the probability that it takes Hadassah less than 3 frames to bowl⍭ Generate me a similar question◊

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