Question

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A student is selected randomly from a class. The probability that this student likes hamburger is 0.78. and the probability that this student likes both hamburger and fried chicken is 0.65. Given that there is one student in the class who likes hamburger, find the probability that this student also likes fried chicken.​

Answer 1

Probability that this student also likes fried chicken is 0.833.

Step-by-step explanation:

We are given that a student is selected randomly from a class. The probability that this student likes hamburger is 0.78. and the probability that this student likes both hamburger and fried chicken is 0.65.

Let the Probability that student likes hamburger = P(H) = 0.78

Probability that student likes fried chicken = P(C)

Probability that student likes both hamburger and fried chicken = $P(H \bigcap C)$ = 0.65

Now, we have to find the probability that this student also likes fried chicken given that the student likes hamburger = P(C / H)

As we know that the conditional probability of P(A/B) is given by the formula;

                               P(A/B) =  $\frac{P(A \bigcap B)}{P(B) }$

Similarly, P(C / H) = $\frac{P(H \bigcap C)}{P(H)}$

                             = $\frac{0.65}{0.78}$ = 0.833

Therefore, the required probability is 0.833.