Question

) Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10. (a) What is the probability that professor will arrive at place B

Answer 1

Complete Question

Professor Jin wants to travel from place A to place B without a map. There are four ways lead away from place A. If road I is selected, the probability of arriving place B is 1/8; if road II is selected, the probability of arriving place B is 1/6; if road III is selected, the probability of arriving place B is 1/4; and if road IV is selected,the probability of arriving place B is 9/10.

(a) What is the probability that professor will arrive at place B?

(b) If Professor Jin arrives at place B, what is the probability that she chooses road IV?

Answer:

a

`P(B) = 0.36`

b

`P(4 /B) = 0.62`

Explanation:

From the question we are told that

The number of ways from A to B is n = 4

The probability if road 1 is selected is
`P(1) = (1)/(8)`

The probability if road 2 is selected is
`P(2) = (1)/(6)`

The probability if road 3 is selected is
`P(3) = (1)/(4)`

he probability if road 4 is selected is
`P(4) = (9)/(10)`

The probability that professor will arrive at place B is mathematically represented as

`P(B) = (1)/(n) * P(1) + (1)/(n) * P(2) + (1)/(n) * P(3)+ (1)/(n) * P(4)`

`P(B) = (1)/(4) * (1)/(8) + (1)/(4) * (1)/(6) + (1)/(4) * (1)/(4) + (1)/(4) * (9)/(10)`

`P(B) = 0.36`

If Professor Jin arrives at place B, what is the probability that she chooses road IV is mathematically represented as

`P(4 /B) = ( (1)/(n) * P(4))/(P(B))`

=>
`P(4 /B) = ( (1)/(4) * (9)/(10) )/(0.36)`

=>
`P(4 /B) = 0.62`