Question

Will crown best answer

Answer 1

0.7143

Explanation:

we shall analyze the table given. we are to find the probability that the chosen student is male, or has a grade of A. this means the union of these two probabilities.

let the event that the student is a male be A, and the event that the student has an A be B.

recall the formula:

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

where
`P(A\cup B)` means A or B, and
`P(A\cap B)` means A and B.

here, we need to find
`P(A), P(B), P(A\cap B)`. lets find them one by one.

`P(A)` here is the probability that the chosen student is male. of the 49 students, 20 are male. So,
`P(A)=(20)/(49)`.

next,
`P(B)` is the probability that the chosen student has an A. of the 49 students, again 20 have an A. so,
`P(B)=(20)/(49)`.

lastly,
`P(A\cap B)` is the probability that the chosen student is both male and has an A. of the 49 students, 5 of them satisfy this. hence,
`P(A\cap B)=(5)/(49)`.

finally, we can calculate the union probability, being:

`P(A\cup B)=(20)/(49)+(20)/(49)-(5)/(49)=(35)/(49)=(5)/(7)`, equal to 0.7143 to 4 decimal places.