Spin the Big Wheel! (probability)

Spinner :

Spinner has 4 equal sectors colored yellow, blue, green, red .

Illustrations:

Q1 : Spinner has 4 equal sectors colored yellow, blue, green , red . What are the

chances of landing on red after spinning a spinner.

Solution:

Let sample space be S and event of getting blue color be E.

S = yellow, blue, green, red

n(S) = 4

E = red

n(E) = 1

P(E) = 1/4 .

Q2 : If two spinners are spin, what is the probability of landing

i) Two different colors ii) two same colors .

Solution :

Let sample space be S, then n(S) = 4² =16

i) Let E₁ be the event of landing two different colors when two spinners are spin.

n(E₁) = 4 x 3 = 12

P(E₁) = n(E₁)/n(S)

= 12/16 =3/4

ii) Let E₂ be the event of landing two same colors.

n(E₂ ) = 4

P(E₂) = n(E₂)/n(S) = 4/16 =1/4

Q3 : When two dice are thrown, find the probability of getting equal numbers .

Solution :

Let S be the sample space and E be the event of getting equal numbers.

S = (1,1), (1,2), (1,3),......(1,6),

(2,1), (2,2), ...............(2,6),

.........................................

(6,1), (6,2) .................(6,6)

n(S) = 36

E = (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

n(E) = 6

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

= 6/36

= 1/6 .

Q4 : In a single throw of two dice find the probability of throwing a sum (i) 10 (ii) which

is a perfect square.

Solution :

Let S be the sample space.

n(S) = 36.

(i) Let E₁ be the event of getting the sum 10

Then E₁ = (4,6) , (5,5), (6,4)

n(E1)= 3

P(E₁ ) = n(E₁)/n(S)

= 3 /36

= 1/12

(ii) LEt E₂ be the event of getting a perfect square

least sum is 2 and maximum sum is 12

perfect squares in [2, 12] are 4, 9

so, E₂ = (1,3), (2,2), (3,1), (3,6), (4,5),(5,4), (6,3)

n(E₂) = 7

P(E₂ )= 7/36

Q5 : When an unbiased coin is tossed 5 times, find the probability of getting head atleast

once.

Solution :

Let S be the sample space when a coin is tossed 5 times.

Then n(S) = 2⁵

Let E be event of getting atleast one head, then E^c be the event of not getting

atleast one head , i. e. getting all tails.

n(E^c ) = 1

P(E^c) = 1/2⁵

P(E) = 1 - P(E^c)

=1 - (1/2⁵ )

=1 - 1/32

= 31/32 .

Q6 : A and B throw with three dice. If A throws 16, find B's chance of throwing a higher number .

Solution :

If three dice are thrown the minimum sum on them is 3 and maximum sum is 18

If A throws 16 then B must throw 17 or 18 in order to get higher than A.

Let sample space be S.

n(S) = 6³

=216

B = (5,6,6), (6,5,6), (6,6,5), (6,6,6)

n(B) = 4

P(B) = 4/216 = 1/54