Suppose that a card game uses a special deck of cards made of 30 cards, with 6 of them being each of 5 different colours, one of which is red. For examples there are 6 red cards, 6 green cards and so on for each colour.Suppose you randomly pick 2 cards from the deck without replacement.What is the probability that neither card is red?

To find the probability that neither card is red, we need to consider the total number of ways to draw 2 cards from the deck and the number of ways to draw 2 cards that are not red.

Step 1: Find the total number of ways to draw 2 cards from the deck.

The total number of ways to draw 2 cards from a deck of 30 is given by the combination formula 30 choose 2, which is denoted as 30C2.

30C2 = 30! / [(30-2)! * 2!] = (3029) / (21) = 435

So, there are 435 different ways to draw 2 cards from the deck.

Step 2: Find the number of ways to draw 2 cards that are not red.

There are 6 red cards in the deck, so there are 30 - 6 = 24 cards that are not red. The number of ways to draw 2 cards from these 24 is given by the combination formula 24 choose 2, which is denoted as 24C2.

24C2 = 24! / [(24-2)! * 2!] = (2423) / (21) = 276

So, there are 276 different ways to draw 2 cards that are not red.

Step 3: Calculate the probability.

The probability that neither card is red is the number of ways to draw 2 cards that are not red divided by the total number of ways to draw 2 cards.

So, the probability is 276 / 435 = 0.634 (rounded to three decimal places).

Therefore, the probability that neither card is red is approximately 0.634 or 63.4%.