Question

There are 5 cards in box with numbers 1 to 5 written on them.If 2 cards are picked out from the box.write all possible outcomes.find probability of getting both even numbers

Answer 1

Answer:

1) Possible Outcome:{(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)}

2) Probability:1/10

Step-by-step explanation:

There are 5 cards in box with numbers 1 to 5 written on them.

If 2 cards are picked out from the box.

1)write all possible outcomes:

{(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)}

2) find probability of getting both even numbers

Favourable outcome : since even number cards are 2:{2,4}

way to choose 2 even cards from 2 even cards=

$^{n} C_r = ^{2}C_2 = 1$

Total outcomes

$^{5} C_2 = \frac{5!}{2!\times 3!} \\ \\ = \frac{5 \times 4 \times 3!}{2 \times 3!} \\ \\ = 10$

Probability of getting both even cards

$P(getting\:both\:even\:cards)= \frac{1}{10}$

Hope it helps you.