Question

A box contains $100$ red cards, $200$ yellow cards and $50$ blue cards. If a card is drawn at random from the box, then find the probability that it will be (i) a blue card (ii) not a yellow card (iii) neither yellow nor a blue card.

Answer 1

Total no. of cards in the box is $350$ $(100$ red, $200$ yellow and $50$ blue$)$

Solution(i):

No. of blue cards in the box is $50$

Therefore, ${}^{50}{C}_1$( Selecting $1$ out of $50$ items) times out of ${}^{350}{C}_1$( Selecting $1$ out of $350$ items) a blue card is picked.

Let $E$ be the event of drawing a blue card from bag

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^{50}{C}_1}{{}^{350}{C}_1}$$=\frac{50}{350}$$=\frac{1}{7}$

Solution(ii):

No. of non-yellow cards in box is $150$ $(100$ red and $50$ blue$)$

Therefore, ${}^{150}{C}_1$( Selecting $1$ out of $150$ items) times out of ${}^{350}{C}_1$( Selecting $1$ out of $350$ items) a non-yellow card is picked.

Let $E$ be the event of drawing a non-yellow card from bag

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^{150}{C}_1}{{}^{350}{C}_1}$$=\frac{150}{350}$$=\frac{3}{7}$

Solution(iii):

No. of neither yellow nor blue card in box is $100$ $(100$ red cards$)$

Therefore, ${}^{100}{C}_1$( Selecting $1$ out of $100$ items) times out of ${}^{350}{C}_1$( Selecting $1$ out of $350$ items) a neither yellow nor blue card is picked

Let $E$ be the event of drawing neither yellow nor blue cardfrom the box

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^{100}{C}_1}{{}^{350}{C}_1}$$=\frac{100}{350}$$=\frac{2}{7}$