An experiment of drawing a random card from an ordinary playing cards deck is done with replacing it back. This was done ten times. Find the probability of getting $2$ spades, $3$ diamond $3$ club and $2$ hearts.

0.024

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0.029

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0.020

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0.032

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Solution

The correct option is A $0.024$
Probability of getting a spade $= \frac{13}{15} = 0.25$
Probability of getting a diamond $= \frac{13}{15} = 0.25$
Probability of getting a club $= \frac{13}{15} = 0.25$
Probability of getting a heart $= \frac{13}{15} = 0.25$
Using Multinomial theorem, we have
Desired probability $= \frac{10!}{(2! 3! 3! 2!)} {(0 .25)}^{2} {(0.25)}^{3} {(0.25)}^{3} {(0.25)}^{2} = 0.024$
So, option A is correct.

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An experiment of drawing a random card from an ordinary playing cards deck is done with replacing it back. This was done ten times. Find the probability of getting 2 spades, 3 diamond 3 club and 2 hearts.

An experiment of drawing a random card from an ordinary playing cards deck is done with replacing it back. This was done ten times. Find the probability of getting $2$ spades, $3$ diamond $3$ club and $2$ hearts.