Question

There are 4 blueberry, 6 raisins, and 2 plain bagels in a bag. Mike randomly selects two bagels without replacing the first bagel. Find the probability that he selects a raisin bagel and then a plain bagel

Answer 1

The probability that he selects a raisin bagel and then a plain bagel is
`\frac1{11}`.

Explanation:

Probability:

The ratio of the number of outcomes of favorable event to total number of all possible outcomes is called probability of the favorable event.

`Probability=\frac{\textrm{The number of favorable outcomes}}{\textrm{Total number of all possible}}`

Given that, there are 4 blueberry, 6 raisins and 2 plain bangles in a bag.

Total number of bangles= (4+6+2)

= 12

The probability that he selects a raisin

`=\frac{\textrm{Number of raisin bangles}}{\textrm{Total number of bangles}}`

`=(6)/(12)`

`=\frac12`

Total number of remaining bagels is =(12-1)=11

After selecting a raisin bagel,the probability that he selects a plain bangle is

`=\frac{\textrm{Number of plain bangles}}{\textrm{Total number of bangles}}`

`=(2)/(11)`

Selecting of a raisin bangle and a plain bangle are both independent event.

The probability that he selects a raisin bagel and then a plain bagel is

`=\frac{1}2*(2)/(11)`

`=\frac1{11}`