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

Answer:

Step-by-step explanation:

SOLUTION :  

GIVEN : Number of red cards  = 100

Number of yellow cards = 200

Number of blue cards = 50

Total number of cards in a box = 100 + 200 + 50  = 350

Total number of outcomes = 350

(i) Let E1 = Event  of selecting that a card drawn is blue

Number of blue cards = 50

Number of outcome favourable to E1 = 50

Probability (E1) = Number of favourable outcomes / Total number of outcomes

P(E1) = 50/350 = 1/7

Hence, the required probability of getting a card drawn is blue, P(E1) = 1/7  

(ii) Let E2 = Event  of selecting that a card drawn is not a yellow card  

Number of cards which are not yellow = 100 + 50 = 150

Number of outcome favourable to E2 = 150

Probability (E2) = Number of favourable outcomes / Total number of outcomes

P(E2) = 150/350 = 15/35 = 3/7  

Hence, the required probability of getting a card drawn is not a yellow card , P(E2) = 3/7  

(iii) Let E3 = Event  of selecting that a card drawn is neither yellow nor blue  

Number of cards which are neither yellow nor blue  = 100  

Number of outcome favourable to E3 = 100

Probability (E3) = Number of favourable outcomes / Total number of outcomes

P(E2) = 100/350 = 10/35 = 2/7  

Hence, the required probability of getting a card drawn is neither yellow nor blue , P(E3) = 2/7  

HOPE THIS ANSWER WILL HELP  YOU….

Answer 2

Hi there!
Here's the answer:

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Given,
A box contains 100 red cards, 200 yellow cards and 50 blue cards.

A card is drawn at random

Let S be Sample space

n(S) - No. of ways of drawing a card from 350 cards
n(S) = 350C1 = 350

Let E1 be the Event that card drawn is a blue card

n(E1)- No. of favorable cases for occurrence of Event E1
n(E1)= 50C1 = 50

Let E2 be the Event that card drawn is not a yellow card
E2 ={ (Red cards), (Blue cards)}

n(E2)- No. of favorable cases for occurrence of Event E2

n(E2)= (100+50)C1 = 150C1 = 150

Let E3 be the Event that card drawn is neither yellow nor a blue card.

E3 = {(Red cards)}

n(E3)- No. of favorable cases for occurrence of Event E3

n(E3) = 100C1 = 100

$Probability = \frac{No.\: of\: Favourable\: Outcomes}{Total\: No.\: of\: Outcomes}$

(i) Probability of getting a blue card

$P(E1) = \frac{n(E1)}{n(S)}$

$P(E1) = \frac{50}{350} = \frac{1}{7}$

•°• Required Probability = $\frac{1}{7}$

(ii) Probability of getting
not a yellow card
$P(E2) = \frac{n(E2)}{n(S)}$

$P(E2) = \frac{150}{350} = \frac{3}{7}$

•°• Required Probability = $\frac{3}{7}$

(iii) Probability of getting neither a yellow nor a blue card

$P(E1) = \frac{n(E1)}{n(S)}$

$P(E1) = \frac{100}{350} = \frac{2}{7}$

•°• Required Probability = $\frac{2}{7}$

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