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

Answer:

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

Step-by-step 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

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

$=\frac{6}{12}$

$=\frac12$

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

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

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

$=\frac{2}{11}$

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

$=\frac{1}2\times\frac{2}{11}$

$=\frac1{11}$