Max has a bowl of 30 grapes, of which 60% of which are red grapes and 40% are white grapes. If he pulls two grapes randomly from the bowl without replacement then which of the following is the probability that they are both red?

51/145

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen added to the probability that the event will not happen gives 1. In other words, the outcome of a probability cannot exceed 1.

Given that the bowl has 30 grapes of which 60% of which are red grapes and 40% are white grapes, the number of;

red grapes

= 60% * 30

= 18

white grapes

= 40% * 30

= 12

If he pulls two grapes randomly from the bowl without replacement then the probability that they are both red is the product of the probability of the first being red multiplied by the probability of the second being red.

Probability of the first being red

= 60% = 3/5

Probability of the second being red (without replacement of the first)

= (18 - 1) / (30 - 1)

= 17/29

the probability that they are both red

= 3/5 * 17/29

= 51/145