Probability - II

PARAGRAPH 1Football teams T
_{1} and T_{2} have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_{1} winning, drawing and losing a game against T_{2} are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_{1} and T_{2}, respectively, after two games. |

P(X > Y) is

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JEE Advanced 2016

PARAGRAPH 1Football teams T
_{1} and T_{2} have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_{1} winning, drawing and losing a game against T_{2} are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_{1} and T_{2}, respectively, after two games. |

P(X = Y) is

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JEE Advanced 2016

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JEE Advanced 2012

A bubble when exposed to air can undergo either of the following events after completion of every second

(I) it splits into 3 bubbles, probability of which is$\frac{2}{3}$

(II) it remains as it is, probability of which is $\frac{2}{9}$

(III) it bursts, probability of which is $\frac{1}{9}$

Either of the events continues to occur every second if the bubble splits or remain as it is. Choose the option corresponding to the correct matching of elements from List-I and List-II.

(I) it splits into 3 bubbles, probability of which is$\frac{2}{3}$

(II) it remains as it is, probability of which is $\frac{2}{9}$

(III) it bursts, probability of which is $\frac{1}{9}$

Either of the events continues to occur every second if the bubble splits or remain as it is. Choose the option corresponding to the correct matching of elements from List-I and List-II.

List-I |
List-II |
||

P. | The probability that all bubbles bursts immediately after completion of 2 seconds is | 1. | $\frac{8}{81}$ |

Q. | The probability that after 2 seconds, exactly 9 bubbles are in air is | 2. | $\frac{8}{243}$ |

R. | The probability that maximum bubbles are there after 3 seconds is | 3. | $\frac{56}{{3}^{7}}$ |

S. | The probability that after 2 seconds exactly 6 bubbles are in air is | 4. | $\frac{16}{81}$ |

5. | $\frac{8}{27}$ | ||

6. | ${\left(\frac{2}{3}\right)}^{13}$ | ||

7. | $\frac{4}{9}$ |

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JEE Advanced 0