8 can be thrown with a pair of dice in the following ways (2,6), (6,2), (4,4), (5,3), (3,5) So, Probability of throwing ‘8’ = 5/36 And Probability of not throwing ‘8’ = 31/36 And 7 can be thrown with a pair of dice in the following ways (1,6), (6,1), (2,5), (5,2), (3,4), (4,3) So, the probability of throwing a ‘7’ = 6/36= 1/6 And Probability of not throwing ‘7’ = 5/6 Let E1 be the event of the throwing a ‘8’ in a single throw of a pair of dice and E2 be the event of throwing a ‘7’ in a single throw of a pair of Dice Then P(E1) = 5/36 , P(E2) = 1/6 And P(¯E1)= 31/36, P(¯E2) = 5/6 Tom wins if he throws ‘8’ in first or third or fifth............ throws. Probability of Tom throwing a ‘8’ in First throw = P(E1) = 5/36 And Probability of Tom throwing a ‘8’ in third throw = P(¯E1 ∩ ¯E2 ∩ E1 ) = P(¯E1) × P(¯E2) × P(E1) = 31/36 × 5/6 ×5/36 Similarly, Probability of Tom throwing a ‘8’ in fifth throw = P(¯E1) × P(¯E2) × P(¯E1) × P(¯E2) × P(E1) = (31/36)^2×(5/6)² ×5/36 Hence, Probability of winning of Tom = P[E1∪(¯E1 ∩ ¯E2 ∩ E1)∪ (¯E1∩ ¯E2 ∩ ¯E1∩¯E2∩ E1)∪……. ] = P[E1+(¯E1 ∩ ¯E2 ∩ E1)+ (¯E1∩ ¯E2 ∩ ¯E1∩¯E2∩ E1)+⋯…. ] Sum of n terms of Geometric Progression , if r < 1 = a/(1-r) ∴ Probability of winning of Tom = (5/36)/(1-(31/36 × 5/6)) = 30/61 Thus, Probability of winning of Jerry = 1 - 30/61 = 31/61
Fruit of mango is known as
Which of the following is not a correct statement?
Licensing and registration of food business in FSSAI are covered under which section:
______________ formulated water grid
Hue denotes:
bhindi yellow vein clearing disease is transmited by
Central Avian Research Institute ,Izzatnangar was established in the year
Which type of clay mineral chlorite is
Which element is responsible for nodulation in legumes?
Mid season pear cultivars for high hills of Himachal Pradesh are
A. Bartlett
B. Starkrimson
C. Flemish Beauty
D. Conference<...