Mathematics: The probability that a battery will last 10 hours or more is 80%, but the probability that a battery will last 15 hours or more is only 15%. What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more

The probability that a battery will last 10 hours

jvsome8

02.07.2021

0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Lasting 10 hours or more.

Event B: Lasting 15 hours or more.

The probability that a battery will last 10 hours or more is 80%.

This means that P(A) = 0.8

Probability of lasting 10 hours or more and 15 hours or more.

This is the probability of lasting 15 hours or more(if it has lasted 15 or more, it has lasted 10 or more).

The probability that a battery will last 15 hours or more is only 15%, which means that $P(A \cap B) = 0.15$

What is the probability that a battery will last 15 hours or more given that it has lasted 10 hours or more?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.8} = 0.1875$

0.1875 = 18.75% probability that a battery will last 15 hours or more given that it has lasted 10 hours or more.

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zovav1oszg9z

10.06.2020

a11= 3

a12= 7

a13= 20

a21= 1

a22= -4

a23= 9

Step-by-step explanation:

the answer on edge 2020

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