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An infinite triangular grid is drawn on the floor example below). The triangles

ID: 3202454 • Letter: A

Question

An infinite triangular grid is drawn on the floor example below). The triangles are equilateral with sides of 10 cm. A coin of 2 cm in diameter is flipped and lands on the floor. What is the probability that the coin does not cross any grid line? Five-card draw is a poker variant in which a player is dealt five cards. The player can choose to replace 1 - 3 of their cards. Note that the player can choose not to replace any cards at all too. Assume that you are using a standard deck of cards and that you are the only player. What is the probability of getting a flush (five cards of the same suit)?

Explanation / Answer

The probability of flush is :

there are 13 cards of same suit , and there are 4 different types of suits

there are total 52 cards

Thus the number of ways all 5 cards of same suits can be selected = 13C5

This can happen for any type of the suit

thus there are 4*13C5 types of ways fo getting flush

The total number of combiantions for picking 5 cards out of a deck of 52 is: 52C5

.

hence Probability = Number of favorable outcomes / total number of outcomes

Probability = 4 *13C5 / 52C5

Probability = 4 * 13 *12 * 11* 10* 9 / (52 *51 *50 *49 *48)

Probability = 0.0019