Question

Math

Posted 5 months ago

```
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.
$P(F<3)=$
```

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Answer from Sia

Posted 5 months ago

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.

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