WeCP Probability Quiz 1

Explanation :

Then n(S) = no of ways of drawing 2 balls out of (6+4) = ^{14}C_{2} = 91

Let E = event of getting both balls of same colour

 

Then,n(E) = no of ways (2 balls out of 8) or (2 balls out of 6)

= 8C2 + 6C2

= 28 + 15

= 43

Therefore, P(E) = n(E)/n(S) = 43 / 91

Explanation:

We have n(s) = 52C2 = 1326

Let A = event of getting both black cards

B = event of getting both queens

A∩B = event of getting queen of black cards

n(A) = 325,n(B) = 6,n(A∩B) = 4c2 = 1

P(A) = n(A)/n(S) = 325/1326;

P(B) = n(B)/n(S) = 6/1326 and

P(A∩B) = n(A∩B)/n(S) = 1/1326

P(A∪B) = P(A) + P(B) - P(A∩B) = (325+6-1) / 1326 = 330/1326 = 55/221

Explanation :

Total number of possible outcomes = 15+30 = 45

Total number of prizes = 15

p(E) = n(s) / n(E) = 15 / 45 = ⅓

Explanation :

Clearly, there are 52 cards, out of which there are 12 face cards.

P (getting a face card) = 12/52=3/13.

Explanation :

Here S= {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}.

Let E = event of getting at least two heads = {THH, HTH, HHT, HHH}.

P(E) = n(E) / n(S)

= 4/8= 1/2

Explanation :

Clearly, n(S) = 6 x 6 = 36

Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.

Then,E = {(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),(6,6)}

n(E) = 14.

Hence, P(E) = n(E)/n(S) = 14/36 = 7/18

Explanation:

1 year = 365 days . A leap year has 366 days

A year has 52 weeks. Hence there will be 52 Sundays for sure.

52 weeks = 52 x 7 = 364days

366 – 364 = 2 days

In a leap year there will be 52 Sundays and 2 days will be left.

These 2 days can be:

1. Sunday, Monday


2. Monday, Tuesday


3. Tuesday, Wednesday


4. Wednesday, Thursday


5. Thursday, Friday


6. Friday, Saturday


7. Saturday, Sunday

Explanation :

Let   A = Event that A speaks the truth

B = Event that B speaks the truth

 

Then P(A) = 75/100 = 3/4

P(B) = 80/100 = 4/5

p(A-lie) = 1 - 3 / 4 = 1 / 4

p(B - lie) =1 - 4 / 5 = 1 / 5

Now, A and B contradict each other =[A lies and B true] or [B true and B lies

= 7 / 20  =35%

Explanation :

Here n(S) = (6 x 6) = 36

Let E = event of getting a total more than 7

= {(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}

Therefore,P(E) = n(E)/n(S) = 15/36 = 5/12.

Explanation :

A leap year has 52 weeks and two days

Total number of cases = 7

Number of favourable cases = 1

i.e., {Friday, Saturday}

Required Probability = 1/7