Use the following information for all steps in this problem. Input all answers t

Question

Use the following information for all steps in this problem. Input all answers to three decimals places and do not input your answers as a percentage.

Alec is taking both a Statistics course and a Geography course this semester. The probability that he passes his Statistics course is 0.65. The probability that he passes his Geography course is 0.92. These two events (passing Statistics and passing Geography) are independent.

1. What is the probability he passes both classes?

2. What is the probability he passes one class, but fails the other?

3. What is the probability he passes at least one class?

4. What is the probability he passes neither class?

5. What is the probability he passes Statistics and fails Geography?

6. What is the probability he passes Geography and fails Statistics?

Explanation / Answer

The probability that he passes his Statistics course is 0.65

probability that he passes his Geography course is 0.92

1) What is the probability he passes both classes?

0.65+0.92-(0.65*0.92) = 0.598

2) What is the probability he passes one class, but fails the other?

at least one of them passing means if he passes in stastics or in geographyor if both passes

.all these three situations mean at least one has passed.

so first case only passed in statstics (inherently it shows that the failed in geography ) =

prob of failing in geography and prob of passing in geography = (0.65)*(0.65)= 0.4225

second case the situation is reverse. prob of passingin geography and prob of failing in stastics

=0.92*0.92=0.8464

third scenario if both passes .

then prob is 0.65*0.92=0.598

all we get = 0.8464 + 0.4225 - 0.598 =0.6709

3 ) What is the probability he passes at least one class?

P(pass at least one) = P(pass statstics ) + P(pass geography) - P(pass both)

   = 0.65+0.92-0.598= 0.972

4) What is the probability he passes neither class

1-passes in both = 1-0.598= 0.402

5) What is the probability he passes Statistics and fails Geography

0.65 *(1-0.92) = 0.052

6 )What is the probability he passes Geography and fails Statistics?

0.92 * (1- 0.65) =0.322

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